Abstract
The aim of this paper was to generate nanotopological structure on the power set of vertices of simple digraphs using new definition neighbourhood of vertices on out linked of digraphs. Based on the neighbourhood we define the approximations of the subgraphs of a graph. A new nanotopological graph reduction to symbolic circuit analysis is developed in this paper. By means of structural equivalence on nanotopology induced by graph we have framed an algorithm for detecting patent infringement suit.
Highlights
The theory of nanotopology proposed by Lellis Thivagar and Richard (2013a, 2013b), is an extension of set theory for the study of intelligent systems characterized by in sufficient and incomplete information
We believe that nanotopological graph structure will be an important base for modification of knowledge extraction of processing
(iii) The boundary region is defined as BN[V(H)] = UN[V(H)] − LN[V(H)]. Such that, Definition 3.3 Let G be a graph, N(v) be neighbourhood of v in V and H be a subgraph of G, N[V(H)] = {V(G), LN[V(H)], UN[V(H)], BN[V(H)]} forms a topolgy on V(G) called the nanotopology on V(G) with respect to V(H)
Summary
The theory of nanotopology proposed by Lellis Thivagar and Richard (2013a, 2013b), is an extension of set theory for the study of intelligent systems characterized by in sufficient and incomplete information.
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